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An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

In this paper, we investigate a competitive market involving two agents who consider both their own wealth and the wealth gap with their opponent. Both agents can invest in a financial market consisting of a risk-free asset and a risky…

In zero-sum games, the optimal strategy is well-defined by the Nash equilibrium. However, it is overly conservative when playing against suboptimal opponents and it can not exploit their weaknesses. Limited look-ahead game solving in…

Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm…

Can players sustain long-run trust when their equilibrium beliefs are shaped by machine-learning methods that penalize complexity? I study a game in which an infinite sequence of agents with one-period recall decides whether to place trust…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…

Recent work reports that Large Reasoning Models (LRMs) undergo a collapse in performance on solving puzzles beyond certain perplexity thresholds. In subsequent discourse, questions have arisen as to whether the nature of the task muddles an…

Reasoning Language Models, capable of extended chain-of-thought reasoning, have demonstrated remarkable performance on tasks requiring complex logical inference. However, applying elaborate reasoning for all queries often results in…

We study model-based and model-free policy optimization in a class of nonzero-sum stochastic dynamic games called linear quadratic (LQ) deep structured games. In such games, players interact with each other through a set of weighted…

This study reveals how frontier Large Language Models LLMs can "game the system" when faced with impossible situations, a critical security and alignment concern. Using a novel textual simulation approach, we presented three leading LLMs…

The decisions that human beings make to allocate time has significant bearing on economic output and to the sustenance of social networks. The time allocation problem motivates our formal analysis of the resource allocation game, where…

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…

In this paper, we investigate how randomness and uncertainty influence learning in games. Specifically, we examine a perturbed variant of the dynamics of "follow-the-regularized-leader" (FTRL), where the players' payoff observations and…

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent…

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…

Despite impressive advances in large language models (LLMs), existing benchmarks often focus on single-turn or single-step tasks, failing to capture the kind of iterative reasoning required in real-world settings. To address this…

The rapid advancement of large language models has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate the strategic reasoning capabilities of LLMs, game theory, with its concise…

Large Language Models (LLMs) have recently shown a promise and emergence of Theory of Mind (ToM) ability and even outperform humans in certain ToM tasks. To evaluate and extend the boundaries of the ToM reasoning ability of LLMs, we propose…

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…

Large language models (LLMs) are increasingly used both to make decisions in domains such as health, education and law, and to simulate human behavior. Yet how closely LLMs mirror actual human decision-making remains poorly understood. This…